Questions tagged [formation-of-numbers]

For puzzles about forming numbers using other numbers and mathematical operations.

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23
votes
6answers
77k views

Make numbers 1 - 30 using the digits 2, 0, 1, 8

It's 2018 so let's repeat last year's challenge with new digits. This is similar to the "Four fours" puzzle, but using the digits 2, 0, 1 and 8. Rules: Use all four digits exactly once Allowed ...
14
votes
6answers
3k views

Use 2 0 1 and 8 to make 67

Use $2$ $0$ $1 $ and $8$ to make the number $67$ RULES You must use all 4 digits. Only the digits 2, 0, 1, and 8 can be used. You can make multi-digit numbers out of the numbers. Examples: 20, 82, ...
3
votes
2answers
2k views

Make numbers 93 using the digits 2, 0, 1, 8

I have a 1 to 100 building challenge with 2, 0, 1, 8, all made but 93 is not made. I need your help! This is similar to the "Four fours" puzzle, but using the digits 2, 0, 1 and 8. Rules: Use all ...
32
votes
18answers
11k views

Use 2, 0, 1 and 8 to make 109

Assemble a formula using the numbers $2$, $0$, $1$, and $8$ in any order that equals 109. You may use the operations $x + y$, $x - y$, $x \times y$, $x \div y$, $x!$, $\sqrt{x}$, $\sqrt[\leftroot{-2}\...
17
votes
2answers
13k views

Write twenty-four from four numbers

Write 24 using the four numbers 1, 3, 4, 6 and basic arithmetic. Explanations: The given are numbers, not digits, so you can't group them using decimal notation. For example, you can't create the ...
44
votes
10answers
148k views

1 2 3 4 5 6 7 8 9 = 100

The sequence of numbers $1\ 2\ 3\ 4\ 5\ 6\ 7\ 8\ 9$ has the property that you can insert mathematical operators in between the numbers from $1$ to $9$ and make the expression evaluate to 100. For ...
22
votes
10answers
14k views

Make 5 5 5 5 = 19 [closed]

Can you find a way to make: $5\ 5 \ 5 \ 5 = 19$ by adding any operations or symbols? You can use only these symbols: $+,\ -,\ *,\ !,\ /,\ \hat\, ,\ ()$. It is limited to this list, and ...
14
votes
3answers
627 views

Hiker's Cabin Mystery | Pt. II

See Part I | See Part III Nice one, @GarethMcCaughan! Finally, you've gotten into his computer using the password you managed to decode from his clues... but there's another issue! There is a ...
1
vote
1answer
197 views

1984 - take the digits 1,9, 8 and 4 and make 246

Next year is the 70th anniversary of the publication of the book 1984 by George Orwell. Here is a puzzle to start the anniversary celebrations off a bit early ... Warm up Can you assemble a formula ...
14
votes
12answers
265k views

1 2 3 4 5 6 7 8 9 = 1

This question inspired me to write the same puzzle but instead replace the "= 100" with "= 1" with similar requirements and restrictions. What is the expression with the fewest number of operators ...
13
votes
16answers
10k views

A truly amazing way of making the number 2016

Find a mathematical expression that yields the value $2016$ while obeying the following rules: Each of the digits $1,2,3,4,5,6,7,8,9$ is used exactly once Decimal points are allowed You ...
14
votes
3answers
1k views

If 6 was 9, or 100 was 64, or M was N

         Now if a 6,          Turned out to be 9,          I don’&...
2
votes
10answers
15k views

Make numbers 1-30 using 2, 0, 1, 9

This is very similar to the 2, 0, 1, 8 problem. Just try to make all numbers 1-30 using the digits 2, 0, 1, 9. Rules: Use all four digits exactly once Allowed operations: +, -, x, ÷, ! (factorial), ...
19
votes
2answers
995 views

Self-intro to mo-Roman numerals

Here come mo -Roman numerals — just like Roman numerals, only mo’ so.   (Explained as we go.)   What number can spell itself in two different ways ...
18
votes
1answer
1k views

New Mathematics forever

This has been (renamed and) refocused on boboquack’s unforeseen solution, which deserves its own puzzle. Right when you thought the good old days of New Mathematics were safely dusted, ...
5
votes
4answers
1k views

Making 1-50 from 2016

Make the numbers 1-50 using the numbers 2 0 1 6 in the given order. 1.You must use all four digits. 2.You may not use any other numbers. 3.You may use +, -, x, ÷, square root, squaring and cubing, ...
7
votes
4answers
2k views

A truly amazing way of making every possible positive integer

This is a follow-up to "A truly amazing way of making the number 2016": For every positive integer $n$, find a mathematical expression that yields the value $n$ while obeying the following rules:...
4
votes
1answer
235 views

The Autonumerigram Challenge [duplicate]

Some phrases both refer to a number, n, and are comprised of n alphabetic characters. I call any such phrase an autonumerigram. For example, four has 4 letters seven plus seven has 14 letters ...
4
votes
4answers
574 views

Twos For Thought

How many twos do you need to get to the number $100$ exactly? Example: $22+22+22+22+2^2+2^2+2^2$ This example method uses 14 twos and is obviously not ideal. Can you find a way that uses the least ...
-1
votes
2answers
302 views

Coppers - Make 24 [closed]

The make-24 puzzle is an oldie, but a very fun one at that. Given four different numbers, produce—through a sequence of operations upon only those four numbers—the number twenty-four. For example, ...
27
votes
4answers
35k views

Create all numbers from 0-100 only using all of 1,2,3,4 and 5

Create all numbers from 0-100 only using 1,2,3,4 and 5. No repeats and you have to use each number. Also, you can use any operation. I've only gotten to 50 by pure brute force. I think that this might ...
62
votes
24answers
20k views

Make 0 0 0 0 = 8

Can you find a way to make: $0\ 0 \ 0 \ 0 = 8$ by adding any operations or symbols? You can use only these symbols: $+,\ -,\ *,\ !,\ /,\ \hat\, ,\ ()$. It is limited to this list, and ...
26
votes
6answers
25k views

The 10,958 Problem

Here is the task: Write down 10958 using all 1-9 digits in ascending order and only one time. You are allowed to: 1) group digits into numbers 2) use 5 basic operations: + - * / ^ ("^" ...
40
votes
16answers
5k views

What is the smallest set of letters that can spell any integer? [closed]

Today my 9-year-old nephew told me that he can spell any integer in English using only 9 letters. This is how he's doing it: ...
13
votes
5answers
3k views

What is the smallest positive integer, which can not be written without repetitions of digits and using arithmetics only?

Suppose you are allowed to use all 10 digits (0,1,2,...9) at most once each; 4 arithmetic operations ($-$,$+$,$\times$,$\div$), each any number of times; parenthesises to group operations; and you can ...
29
votes
13answers
14k views

10 9 8 7 6 5 4 3 2 1 = 2016

Add the four basic operators $\times\div+\,\;-$ and optionally brackets to: $10 \quad 9 \quad 8 \quad 7 \quad 6 \quad 5 \quad 4 \quad 3 \quad 2 \quad 1$ To get the total $2016$. Rules: We are ...
19
votes
17answers
9k views

Number 88 from the digits 2, 0, 1 and 7?

Can you use the digits 2, 0, 1 and 7 each only once to create the number 88?
9
votes
7answers
50k views

Make numbers 1 - 32 using the digits 2, 0, 1, 7

This is similar to the "Four fours" puzzle, but using the digits 2, 0, 1 and 7. Rules: Use all four digits exactly once Allowed operations: +, -, x, ÷, ! (factorial), exponentiation, square root ...
30
votes
1answer
770 views

Integers around a circle with consecutive pairs adding to a square

The integers 1 to 50 are placed around a circle in such a way that the sum of any two of them which are adjacent is a perfect square. Of these integers, the even numbers are then removed. Restore them....
15
votes
2answers
613 views

Ode to convergence

Taking a numeral core (digits: a non-quad four) digits I ordered, then lesser I minused, till evolve I couldn't more. What is this unfathomably clunky poem all about?
11
votes
11answers
10k views

Make 6 5 4 3 = 81

Can you find a way to make: 6 5 4 3 = 81 by concatenation and/or adding any of (and only) these mathematical operators: + - × ! ÷ ^ standard parentheses () You cannot add other numbers to the ...
8
votes
3answers
5k views

How to make 21?

How do you make $21$ from the numbers $1$, $5$, $6$, and $7$? You can use the operations of addition, subtraction, multiplication and division, as well as brackets. You must use each number exactly ...
3
votes
1answer
145 views

Another loop of integers with consecutive terms adding to a square

The integers 1 to 50 are placed around a circle in such a way that the sum of any two of them which are adjacent is a perfect square. Of these integers, all but the prime integers were removed. ...
34
votes
4answers
3k views

Display a number using a scientific calculator with most keys are stuck

Your have a scientific calculator such that most of the keys are unable to be pressed. The only keys that work are those for the functions $$ x^2 \;\; \sqrt{x} \;\; x!\;\; \exp\;\; \ln\;...
21
votes
12answers
5k views

Make 1998 using the least possible digits 8

Make the number 1998 using the minimum amount of digits 8. Your allowed operations are +, -, *, /, ^, % (percent). You need not use only integers 8: 88 and the likes are acceptable. You must only ...
13
votes
5answers
3k views

Make 2008 from Φ (Golden Ratio)

I know that questions of the form "Use [arbitrary set of numbers] to make 2018" seem to be not very well recieved in the last days. That's why this puzzle is about making 2008. But instead of using ...
11
votes
7answers
1k views

Fill in the boxes to get the right equation

Here is a math puzzle I had a little bit of hard time with No computers please There is a solution without inverting 6 to 9
9
votes
2answers
10k views

Make 10 out of 1, 1, 5 and 8

A friend of mine shared a puzzle with me this evening. Using the numbers 1, 1, 5 and 8 exactly once, and the basic operations (+, -, /, *) and (optionally) parentheses, form an expression which ...
5
votes
3answers
3k views

Express the number $2015$ using only the digit $2$ twice

Can you use only two instances of the digit $2$, along with the mathematical operations below, to create an expression that evaluates to $2015$? Allowed operations: arithmetic operations: addition ($...
4
votes
1answer
2k views

Expressing numbers using 0, 1, 2, 3, and 4

The least number that cannot be written using the numbers 0, 1, 2, and 3, each exactly once, and any combination of standard arithmetic operations (including factorials) is 41. What is the least such ...
1
vote
5answers
272 views

Create all numbers from 1-100 by using 1,3,3,7

Create all the numbers from $1$ to $100$ using the numbers $1,$$3,$$3,$ and $7.$ You can only use each number once, except for the $3,$ of which you have two. You can use addition $(x+y),$ ...
34
votes
5answers
7k views

Rendering the number 10,958 with the string 1 2 3 4 5 6 7 8 9

Brazilian mathematician Inder Taneja has found a way of expressing every number between 1 and 11,111, except 10,958, by inserting mathematical operators in between the numbers 1 2 3 4 5 6 7 8 9 and ...
11
votes
4answers
4k views

Use 1 9 6 2 in this order to make 75

I'm looking for a solution to make number $75$ with numbers $1$ $9$ $6$ $2$ in that order and the same rules as in Use 2 0 1 and 8 to make 67. Here a copy of those rules: You must use all 4 digits. ...
10
votes
6answers
2k views

Maximize the number of factorials in your solution to 6 5 4 3 = 1

Using the same rules as Make 6 5 4 3 = 1, but maximize the number of factorials. You may not take the factorial of 1 or 2. This is harder than it looks. A great answer has six factorials, an ...
8
votes
1answer
874 views

IBM Research Puzzle – 5-ops implementation of erasure code

I found this interesting puzzle on IBM Research Puzzling Page called Ponder This; specifically, here. Design a storage system that encodes 24 information bits on 8 disks of 4 bits each, such that: ...
8
votes
3answers
1k views

$\pi$ Day puzzle one to twenty

Create the numbers from 1 to 20 Using $\pi$ Normal arithmetic operation $+ - * /$ Square root $\surd$ Exponential $(X^Y)$ Negative() minus sign $-$ Floor() function, express between $[ x ]$ $[ ...
6
votes
8answers
548 views

Make $1,\dots,15$ using $3, 9, 9, 9$

This was inspired by many puzzles that use three/four numbers to create other numbers. I chose these numbers in particular because of this post. Can you find a way to make all the natural numbers ...
6
votes
18answers
5k views

Use the numbers 1-9 to equal 1150 [closed]

Not sure if this is too hard, but it's a more or less simple math puzzle. Use the numbers $1,2,3,4,5,6,7,8,9$ to get an answer of 1150. You can use the operators $+,-,*,/,\hat{}$ You can use ...
5
votes
3answers
8k views

Make numbers 1-100 with only four 8s

Make numbers 1, 2, 3, 4, 5,.....100 using only four 8s. You can use multiplication, division, addition, and subtraction. No negatives. You may use exponents. Example: $1 = 8 \times 8 \div 8 \div 8$
-4
votes
10answers
934 views

SafeCracker #3 - We've Been Blocked [closed]

Our Last Safe To Conquer Ok, team, this one might give us a little trouble. Nothing we can't handle though... let's go... This safe model is "The NevaCrak 9000" - the most secure safe there is. ...